1 Answer
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They use cookies to identify the user, and will link this to their database in order to know what is in their cart.

This can be demonstrated by how having items in your cart will not transfer between different browsers (which do not share cookies), and also how if you clear your cookies (specifically one they set called session_id), then your basket will be emptied.

The session_id cookie has an expiry date of a long time in the future, so your cart should not be emptied if you close down your browser. If it did, that would be called a session cookie.

Presumably for a logged-in user, this information is saved instead in their database.